a right triangle has a hypotenuse of length 18 and an angle of 35 degrees, with a side opposite this angle of lenght 4. A second right triangle also has an angle of 35 degrees, with a hypotenuse of length 9. determine the length of the side opposite the 35 degrees angle on the second triangle
In the first triangle, we can use the sine function to find the length of the side opposite the angle of 35 degrees.
sin(35 degrees) = opposite/hypotenuse
sin(35 degrees) = 4/18
To find the length of the side opposite the angle of 35 degrees in the second triangle, we can use the sine function again.
sin(35 degrees) = opposite/9
Since the sine of an angle is the same for all right triangles with that angle, we have:
4/18 = opposite/9
Solving for opposite, we get:
opposite = (4/18) * 9
opposite = 2
So, the length of the side opposite the 35 degrees angle in the second triangle is 2.